When surveys are created and need to be shared to My Groups through the Who can submit to this survey? section under https://survey123.arcgis.com > My Surveys > Survey > Collaborate tab > Share Survey, some groups might not be listed in the section, although they are listed under My Groups within the ArcGIS Online Organization on https://arcgis.com.
Two types of groups are typically not listed in Survey123 Collaborate tab:
Shared Update Groups
Members of shared update groups have elevated privileges, such as the ability to edit the contents of hosted feature layers, alter editor tracking settings, enable or disable attachments, and alter the layer's schema. Therefore, users need to proceed with caution when adding members to this type of group, and most ArcGIS apps do not currently support updating items shared with a shared update group.
Groups that only allow group owner and managers to contribute content
If the group owner chooses this option when the groups are created, members can only view and access group items, but they cannot share their own items with the group.
For the Shared Update Groups, users can share their surveys from within the ArcGIS Online Organization on https://arcgis.com as a workaround.
However, there is no workaround to share surveys to Groups that only allow group owner and managers to contribute content as these groups do not show up in your sharing list in ArcGIS Online either.